Analysis Group
| Faculty | |
|---|---|
| Lolina Alvarez | Harmonic and Functional Analysis: Function spaces, pseudo-differential operators, interplay between harmonic analysis and distribution theory. |
| Tiziana Giorgi | Non-linearPartial Differential Equations: existence, uniqueness (up to a guage) and stability of minimizers to energy funtionals with applications to superconductivity. |
| Doug Kurtz | Harmonic Analysis: maximal functions, singular integrals, multipliers, Littlewood-Paley operators, weighted norm inequalities. |
| Joe Lakey | Harmonic Analysis: time-frequency analysis, wavelets, information theory and applications to signal processing, discrete dynamical systems. |
| Maria Cristina Mariani | Nonlinear Partial Differential Equations:Nonlinear partial differential equations and Stochastic Differential Equations, mathematical finance, mathematical physics, functional analysis and statistical mechanics. |
| Robert Smits | Stochastic and Harmonic Analysis: stochastic differential equations, spectral theory, asymptotic analysis, heat kernels, large deviations, mathematical finance, eigenvalue estimates. |
| Christopher Stuart | Functional Analysis: uniform boundedness principles, barrelled spaces, the topological vector space properties of sequence spaces. |
| Caroline Sweezy | Harmonic Analysis, Complex Analysis, Applications to Partial Differential Equations: weighted inequalities for parabolic and elliptic functions on nonsmooth domains, atomic spaces between H^1 and L^1, Carleson measure conditions, square functions and the exponential square class. |
| Emeritus Faculty | |
| Dick Bagby | Real and Harmonic Analysis: Classical analysis in Euclidean space. Convolution and Fourier multipliers. Continuity properties of operators and bounds for maximal functions in terms of function space norms. Questions of pointwise convergence. |
| Chuck Swartz | Functional Analysis: topological vector spaces, infinite matrices and gliding hump properties in sequence and function spaces, vector and operator valued series, vector valued measures and integrals. |
Group Activities:
With the support of the National Science Foundation, our group organizes the annual New Mexico Analysis Seminar jointly with analysts from the University of New Mexico.